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Simplifying 100a + -1a2 + -1234 = 0 Reorder the terms: -1234 + 100a + -1a2 = 0 Solving -1234 + 100a + -1a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1234 + -100a + a2 = 0 Move the constant term to the right: Add '-1234' to each side of the equation. 1234 + -100a + -1234 + a2 = 0 + -1234 Reorder the terms: 1234 + -1234 + -100a + a2 = 0 + -1234 Combine like terms: 1234 + -1234 = 0 0 + -100a + a2 = 0 + -1234 -100a + a2 = 0 + -1234 Combine like terms: 0 + -1234 = -1234 -100a + a2 = -1234 The a term is -100a. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100a + 2500 + a2 = -1234 + 2500 Reorder the terms: 2500 + -100a + a2 = -1234 + 2500 Combine like terms: -1234 + 2500 = 1266 2500 + -100a + a2 = 1266 Factor a perfect square on the left side: (a + -50)(a + -50) = 1266 Calculate the square root of the right side: 35.580893749 Break this problem into two subproblems by setting (a + -50) equal to 35.580893749 and -35.580893749.Subproblem 1
a + -50 = 35.580893749 Simplifying a + -50 = 35.580893749 Reorder the terms: -50 + a = 35.580893749 Solving -50 + a = 35.580893749 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + a = 35.580893749 + 50 Combine like terms: -50 + 50 = 0 0 + a = 35.580893749 + 50 a = 35.580893749 + 50 Combine like terms: 35.580893749 + 50 = 85.580893749 a = 85.580893749 Simplifying a = 85.580893749Subproblem 2
a + -50 = -35.580893749 Simplifying a + -50 = -35.580893749 Reorder the terms: -50 + a = -35.580893749 Solving -50 + a = -35.580893749 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + a = -35.580893749 + 50 Combine like terms: -50 + 50 = 0 0 + a = -35.580893749 + 50 a = -35.580893749 + 50 Combine like terms: -35.580893749 + 50 = 14.419106251 a = 14.419106251 Simplifying a = 14.419106251Solution
The solution to the problem is based on the solutions from the subproblems. a = {85.580893749, 14.419106251}
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